The discovery of orbital-angular-momentum (OAM) states-of-light beams has resulted in a number of important applications, including microparticle rotation, high-information-density free-space communication protocols, quantum cryptography, and quantum superdense coding. By linearly superposing light states with different OAM quantum numbers possessed by different Gauss-Laguerre (GL) modes under free-space propagation, beams with amplitude, phase, and intensity patterns that merely rotate with propagation while maintaining their transverse shape may be realized.
Imaging systems using an incoherent point-spread function (PSF) that rotates at a uniform rate with changing defocus while maintaining its shape and form approximately have been used to encode the axial coordinate of a point source in a 3D scene with a sensitivity that is nearly uniform over the entire scene. The demonstration of a rotating double-helix PSF by superposing suitably chosen GL modes and its further improvement in light efficiency by pupil-phase optimization have led to methods for generating high-throughput rotating PSFs.
By contrast, for a clear, well corrected imaging aperture in space, the point-spread function (PSF) in its Gaussian image plane has the conventional, diffraction-limited, tightly focused Airy form. Away from that plane, the PSF broadens rapidly, however, resulting in a loss of sensitivity and transverse resolution that makes such a traditional approach untenable for rapid 3D image acquisition. Thus, a major drawback is that the scanning must be done in focus to maintain high sensitivity and resolution as image data is acquired, slice by slice, from a 3D volume with reduced efficiency.